SOLUTION: why it is necessary to reverse the inequality symbol when multiplying both sides of an inequality? what are the basic steps involved in problem-solving and what is the importanc

Question 142681: why it is necessary to reverse the inequality symbol when multiplying both sides of an inequality?
what are the basic steps involved in problem-solving and what is the importance of following these problem solving steps when presented with a problem?
Answer by mangopeeler07(462) (Show Source): You can put this solution on YOUR website!
1. why it is necessary to reverse the inequality symbol when multiplying both sides of an inequality?

This only applies when multiplying or dividing the inequality by a negative number. The inequality has to change because once you have done the operation you are dealing with a whole new range of numbers (on the opposite side of zero). Another way to look at it (if one side is positive and the other is negative) is that the greater/less than sign has to continue to face whichever side (or sign, negative or positive) it faced in the beginning at all times.
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2. what are the basic steps involved in problem-solving and what is the importance of following these problem solving steps when presented with a problem?

This depends on the problem. But for most problems, it is simple:
-identify what you are solving for before you jump into the equation(!*especially if there is more than one variable)
-set up an equation (if it's not set up already)
-isolate the variable

For word problems:
-express everything unknown in terms of a variable (or two or three, if necessary)
-set up an equation according to the information given in the problem

For some, like fractions, you have to:
-find the common denominator
-add or subtract as indicated
-factor(if possible)
-cancel (if possible)

For others, like quadratic, you have to:
-factor
-set equal to zero
-solve for variable

For some, like lines/inequalities, you have to:
-isolate y
-plug in coordinates(if possible) or
-graph (if already solved) including any shading

The steps you take don't ALWAYS have to be in the order that I presented them. As long as you don't LEAVE OUT any steps (doing them in your head is okay, that's not the same as leaving them out).
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